Jin and Sun [1]} have recently showed that for \(c=(\log {n})^{o(1)}\) , a deterministic fully-dynamic \(c\) -edge-connected classes data structure with \(U_c(n)=O(n^{o(1)})\)  and
\(Q_c(n)=O(n^{o(1)})\)  exists. By combining their result
with the fully-dynamic \(c\) -edge-cut algorithm of Thorup [2]} with
\({T_c(n)=O(n^{1/2}\operatorname{poly}{(c)})}\) ,
we obtain the following.
